Page 340 - statbility for masters and mates

328 Ship Stability for Masters and Mates
Shearing stresses are resisted by the material but shearing will take place when the shear stress reaches the ultimate shear stress of the material.
Complementary stress
It has already been stated that when a direct load is applied to a material stresses are created within the material and that the material will remain in equilibrium only so long as the internal forces can resist the stresses created.
Let the bar in Figure 40.3(a) be subjected to tensile load W and imagine the bar to be divided into two parts at section AB.
For equilibrium, the force W on the left-hand side of the bar is balanced by an equal force acting to the right at section AB. The balancing force is supplied by the individual molecular forces which represent the action of the molecules on the right-hand side of the section on those of the left-hand section. Similarly, the force W on the right-hand side of the bar is balanced by the individual molecular forces to the left of the section. Therefore, when an external load W is applied to the bar, at any section normal to the axis of the bar, there are equal and opposite internal forces acting, each of which balances the external force W. The magnitude of the internal forces per unit area of cross-section is called the stress. When the section is well removed from the point of application of the external load then the stress may be considered constant at all parts of the section and may be found by the formula:
Stress(f) Load(W) ;f W Area (A) A
Let us now consider the stresses created by the external load W in a section which is inclined to the axis of the bar. For example, let section CD in Figure 40.3(b) be inclined at an angle y to the normal to the axis of the bar and let the section be suf®ciently removed from the point of application of the load to give uniform stress across the section.
The load transmitted by the section CD, for equilibrium, is equal to the external force W. This load can be resolved into two components, one of which is WEcos y and acts normal to the section, and the other is WEsin y and acts tangential to the section. This shows that for direct tensile or compressive loading of the bar stresses other than normal stresses may be created.
Now let us consider the small block of material abcd in the section on the left-hand side of the plane, as shown in Figure 40.3(c). Let the face ab be coincident with the plane CD and let FN be the internal force normal to this face and FT the internal force tangential to the face. For the block to be in equilibrium the left-hand side of the section must provide two stresses on the face cd. These are FN and FT. Thus the stress FN normal to the face ab is balanced by the stress FN normal to the face cd whilst the two tangential stresses (FT) on these faces tend to produce clockwise rotation in the block. Rotation can only be prevented if an equal and opposite couple is produced